Sponsor:
All the numerical work was carried out using the IBM 3090 computer at the Centro de Investigaciones Energeticas, Medio Ambientales y Tecnol6gicas (CIEMAT), Spain, which we gratefully acknowledge. Two of us (A S and L V) are grateful for financial support from the Universidad Complutense de Madrid and the Direcci6n General de Investigación Cientifica y Tecnica, under grant PB86-000S.

Abstract:

We study the scattering of nonlinear wavepackets in the form of envelope
soli tons by a one-dimensional disordered system. We briefly review the features of the
scattering for linear waves and obtain some results for linear wave packets to demonstrate
their common exponential decay of the transmission coefficient, characterized by a
localization length. We consider the same process for envelope solitons, and we show in
the framework of the simplest model, that, above a certain threshold, strong non linearity
allows undistorted propagation of these wavepackets. We describe how this behaviour
can be obtained, for the nonlinear Schriidinger equation, by means of a simple
independent scattering approach, using results of soliton perturbation theory to compute
one-impurity reflection coefficients in the Born approximation. We derive equations to
describe the transmission of the soli ton parameters and we analyse them in full detail.
The main result of our study is the conclusion that a strong nonlinearity stipulates two
spatial scales in the wavepacket scattering by disordered systems. The first spatial scale
depends on the amplitude and it may be very large, and the second one is the usual
localization length. As a consequence the non linear wavepackets or solitons are much
more stable against disorder than linear ones.